Question

If two parallel planes are cut by a third plane, then the lines of intersection are _________.

Answer 1

Parallel planes are two planes that do not intersect.

Theorem:  If two parallel planes are cut by a third plane, then the lines of intersection are parallel.

In the attached picture you can see two parallel planes P and M that are cut by plane R. The lines of intersection are:

• CD - planes P and R;
• AB - planes M and R.

Conclusion: AB||CD.

Answer: parallel.

Answer 2

If two parallel planes are cut by a third plane, then the lines of intersection are parallel and cannot intersect one another.